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  • $\begingroup$ Could you clarify in what way the windowing makes the periodic extension of your finite sample have statistics that more closely resemble the infinite signal you’re sampling? What statistics? $\endgroup$ Commented Apr 5 at 22:26
  • $\begingroup$ My answer is pretty much an alternate view of Hilmar's. By windowing, you suppress the artifact created by chopping off the infinite signal -- this makes the spectrum that's left more closely resemble the spectrum of the infinite signal -- assuming the infinite signal is stationary, and that you've captured enough of it. $\endgroup$ Commented Apr 6 at 0:36